> ## Documentation Index
> Fetch the complete documentation index at: https://leetcode-py.wisl.dev/llms.txt
> Use this file to discover all available pages before exploring further.

> ## Agent Instructions
> leetcode-py is a Python LeetCode practice environment generator with one CLI: lcpy. It is not a service or platform.
> Each problem is a directory under leetcode/ with README.md, solution.py, test_solution.py, helpers.py, and playground.ipynb. lcpy gen creates them from JSON templates bundled with the package.
> Examples are backed by tests; copy them verbatim.

# Binary Tree Tilt Python Solution with Tests

> Tested Python solution for LeetCode 563 with 16 pytest cases. Generate a practice environment with lcpy.

LeetCode 563, [Easy](/catalog/easy). Topics: [Tree](/catalog/topics/tree), [Depth-First Search](/catalog/topics/depth-first-search), [Binary Tree](/catalog/topics/binary-tree), DP on Trees. [View on LeetCode](https://leetcode.com/problems/binary-tree-tilt/description/).

Generate this problem as a practice environment: tested reference solution, 16 [parametrized pytest cases](/practice/testing), and a playground notebook:

```bash theme={"theme":{"light":"github-light","dark":"github-dark"}}
lcpy gen -n 563   # by problem number
lcpy gen -s binary_tree_tilt   # by problem name
```

## Problem

Given the `root` of a binary tree, return *the sum of every tree node's **tilt***.

The **tilt** of a tree node is the **absolute difference** between the sum of all left subtree node **values** and all right subtree node **values**. If a node does not have a left child, then the sum of the left subtree node **values** is treated as `0`. The rule is similar if the node does not have a right child.

### Examples

![Example 1](https://assets.leetcode.com/uploads/2020/10/20/tilt1.jpg)

```
Input: root = [1,2,3]
Output: 1
Explanation:
Tilt of node 2 : |0-0| = 0 (no children)
Tilt of node 3 : |0-0| = 0 (no children)
Tilt of node 1 : |2-3| = 1 (left subtree is just left child, so sum is 2; right subtree is just right child, so sum is 3)
Sum of every tilt : 0 + 0 + 1 = 1
```

![Example 2](https://assets.leetcode.com/uploads/2020/10/20/tilt2.jpg)

```
Input: root = [4,2,9,3,5,null,7]
Output: 15
Explanation:
Tilt of node 3 : |0-0| = 0 (no children)
Tilt of node 5 : |0-0| = 0 (no children)
Tilt of node 7 : |0-0| = 0 (no children)
Tilt of node 2 : |3-5| = 2 (left subtree is just left child, so sum is 3; right subtree is just right child, so sum is 5)
Tilt of node 9 : |0-7| = 7 (no left child, so sum is 0; right subtree is just right child, so sum is 7)
Tilt of node 4 : |(3+5+2)-(9+7)| = |10-16| = 6 (left subtree values are 3, 5, and 2, which sums to 10; right subtree values are 9 and 7, which sums to 16)
Sum of every tilt : 0 + 0 + 0 + 2 + 7 + 6 = 15
```

![Example 3](https://assets.leetcode.com/uploads/2020/10/20/tilt3.jpg)

```
Input: root = [21,7,14,1,1,2,2,3,3]
Output: 9
```

### Constraints

* The number of nodes in the tree is in the range `[0, 10^4]`.
* `-1000 <= Node.val <= 1000`

## Solution

Reference implementation from [solution.py on GitHub](https://github.com/wislertt/leetcode-py/blob/main/leetcode/binary_tree_tilt/solution.py), full suite in [test\_solution.py](https://github.com/wislertt/leetcode-py/blob/main/leetcode/binary_tree_tilt/test_solution.py):

```python theme={"theme":{"light":"github-light","dark":"github-dark"}}
from leetcode_py import TreeNode


class Solution:
    # Time: O(n)
    # Space: O(h) for the recursion stack
    def find_tilt(self, root: TreeNode[int] | None) -> int:
        total = 0

        def dfs(node: TreeNode[int] | None) -> int:
            nonlocal total
            if node is None:
                return 0
            left_sum = dfs(node.left)
            right_sum = dfs(node.right)
            total += abs(left_sum - right_sum)
            return left_sum + right_sum + node.val

        dfs(root)
        return total
```

## Complexity

| Time | Space |
| - | - |
| O(n) | O(h) for the recursion stack |

## Tags


This documentation is built and hosted on [Mintlify](https://mintlify.com), a developer documentation platform.